Q: What are the factor combinations of the number 584,705?

 A:
Positive:   1 x 5847055 x 11694111 x 5315555 x 10631
Negative: -1 x -584705-5 x -116941-11 x -53155-55 x -10631


How do I find the factor combinations of the number 584,705?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 584,705, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 584,705
-1 -584,705

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 584,705.

Example:
1 x 584,705 = 584,705
and
-1 x -584,705 = 584,705
Notice both answers equal 584,705

With that explanation out of the way, let's continue. Next, we take the number 584,705 and divide it by 2:

584,705 ÷ 2 = 292,352.5

If the quotient is a whole number, then 2 and 292,352.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 584,705
-1 -584,705

Now, we try dividing 584,705 by 3:

584,705 ÷ 3 = 194,901.6667

If the quotient is a whole number, then 3 and 194,901.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 584,705
-1 -584,705

Let's try dividing by 4:

584,705 ÷ 4 = 146,176.25

If the quotient is a whole number, then 4 and 146,176.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 584,705
-1 584,705
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

15115510,63153,155116,941584,705
-1-5-11-55-10,631-53,155-116,941-584,705

More Examples

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